Problem: Solve for $x$ and $y$ using elimination. ${-6x-2y = -36}$ ${5x+2y = 32}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2y$ and $2y$ cancel out. $-x = -4$ $\dfrac{-x}{{-1}} = \dfrac{-4}{{-1}}$ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $\thinspace {-6x-2y = -36}\thinspace$ to find $y$ ${-6}{(4)}{ - 2y = -36}$ $-24-2y = -36$ $-24{+24} - 2y = -36{+24}$ $-2y = -12$ $\dfrac{-2y}{{-2}} = \dfrac{-12}{{-2}}$ ${y = 6}$ You can also plug ${x = 4}$ into $\thinspace {5x+2y = 32}\thinspace$ and get the same answer for $y$ : ${5}{(4)}{ + 2y = 32}$ ${y = 6}$